Several surface investigation techniques, such as X-ray diffraction (XRD), EDX, and optical microscopy, were employed in order to describe the mineral contents in several geomaterials. Space and time resolved optical emission spectroscopy was implemented to analyze the plasma generated by the laser–geomaterial interaction. The values of the plasma parameters (velocity and temperature) were discussed with respect to the nature of the minerals composing the geomaterials and the morphological structure of the samples. Correlations were found between the excitation temperatures of the atomic and ionic species of the plasmas and the presence of calcite in the samples. A mathematical model was built to describe the dynamics in ablation plasma using various mathematical operational procedures: multi structuring of the ablation plasma by means of the fractal analysis and synchronizations of the ablation plasma entities through SL (2R) type group invariance and in a particular case, through self-modulation in the form of Stoler type transformations. Since Stoler type transformations are implied in general, in the charge creation and annihilation processes, then the SL (2R) type group invariance become fundamental in the description of ablation plasma dynamics.